FIG 3 - uploaded by Walaa Seif
Content may be subject to copyright.
![As Fig. 2 but for the even-odd isotonic chains of N = 121,133,157, the odd-even isotonic chains of N = 126,130,154, and the odd-odd isotonic chains of N = 129,131,133 versus the charge number of the parent α emitters. and 133 are presented versus the charge number of the α emitters. The results obtained in the present work for the unfavored decays are compared in the same figure with the corresponding values for the favored decays which were obtained in Ref. [9]. For the unfavored decays, the deduced preformation probability inside the odd-even isotones presented in Fig. 3 ranges between 0.0002 ± 0.0001 ( 255 Md) and 0.0108 ± 0.0062 ( 259 Db). Inside the presented even-odd [odd-odd] isotones, the extracted S expt α has values lying between 0.0040±0.0001 ( 257 Fm) and 0.0761±0.0480 ( 211 Th) [0.0014 ( 220 Ac) and 0.0296 ± 0.0008 ( 220 Fr)]. The corresponding values for the presented favored decays of odd-even, even-odd, and odd-odd nuclei lie between 0.0069 ± 0.0001 ( 211 At) and 0.1180 ± 0.0485 ( 219 Ac), 0.0044 ± 0.0022 ( 263 Sg) and 0.0527 ± 0.0018 ( 217 Po),](profile/Walaa-Seif-2/publication/282612923/figure/fig1/AS:614037452767251@1523409345584/As-Fig-2-but-for-the-even-odd-isotonic-chains-of-N-121-133-157-the-odd-even-isotonic.png)
As Fig. 2 but for the even-odd isotonic chains of N = 121,133,157, the odd-even isotonic chains of N = 126,130,154, and the odd-odd isotonic chains of N = 129,131,133 versus the charge number of the parent α emitters. and 133 are presented versus the charge number of the α emitters. The results obtained in the present work for the unfavored decays are compared in the same figure with the corresponding values for the favored decays which were obtained in Ref. [9]. For the unfavored decays, the deduced preformation probability inside the odd-even isotones presented in Fig. 3 ranges between 0.0002 ± 0.0001 ( 255 Md) and 0.0108 ± 0.0062 ( 259 Db). Inside the presented even-odd [odd-odd] isotones, the extracted S expt α has values lying between 0.0040±0.0001 ( 257 Fm) and 0.0761±0.0480 ( 211 Th) [0.0014 ( 220 Ac) and 0.0296 ± 0.0008 ( 220 Fr)]. The corresponding values for the presented favored decays of odd-even, even-odd, and odd-odd nuclei lie between 0.0069 ± 0.0001 ( 211 At) and 0.1180 ± 0.0485 ( 219 Ac), 0.0044 ± 0.0022 ( 263 Sg) and 0.0527 ± 0.0018 ( 217 Po),
Source publication
The ground state spin and parity of a daughter formed in a radioactive α emitter are expected to influence the preformation probability of the α and daughter clusters inside it. We investigate the α and daughter preformation probability inside odd-A and doubly odd radioactive nuclei when the daughter and parent are of different spin and/or parity....
Similar publications
Low- and medium-spin states have been investigated in the even-even nucleus 84Zr by using in-beam γ-ray spectroscopy via the reactions 59Co(28Si,p2n) and 58Ni(32S,α2p) at beam energies of 99 and 135 MeV, respectively. Several new levels have been identified, including a new even-spin sequence of the γ-vibrational band. The previously known sequence...
Citations
... This in turn enhances the fusion cross section at sub-and near-barrier energies [19,20,27,28]. It influences also the nuclear decays [29][30][31][32][33], determining the corresponding optimum orientations. α decay becomes more complex for deformed emitters due to the fact that both the ground state and low-lying excited states of the daughter nuclei are available for α transitions. ...
... So the multipole expansion of nuclear surface defines the set of in Eq. (3). The odd appear in Eq. (3) if the daughter nucleus has octupole deformation [31,46]. We assume that a spherical α particle interacts with a deformed daughter nucleus that is axially symmetric. ...
... So, at the first stage, it is desirable to use a phenomenological method to evaluate S α . For even-even nuclei considered, the spectroscopic factor for the parent nucleus A(N, Z ) can be estimated, in terms of the numbers of neutrons (N − N 0 ) and protons (Z − Z 0 ) outside the corresponding shell/subshell closures (Z 0 , N 0 ), using the semiempirical formula given by [29,31,49,50] ...
The α decays of even-even Ra, Th, U, and Pu isotopes to ground and excited states of daughter nuclei with neutron numbers of N=130–140 are investigated. These nuclei show some enhanced α-branching ratios to negative-parity states (1−, 3−), compared with the decays to positive-parity states (4+) of comparable energy. This enhancement correlates with appearance of static octupole deformation, rather than spherical nuclear shapes or dynamic asymmetric vibrational states. The highly enhanced branching ratios occur for α decays to the 1− and 3− states of the Ra isotopes with N=134, 136, 138, then to 1− state in Th (N=134–140) and to the 3− state in Rn (N=132–136) isotopes.
... Particularly, some neutron-deficient nuclei around the region Z = 82 in the heavy-ion reaction are often excluded in the in-beam γ-ray experiments [17]. On the other hand, all theoretical probes on this shell closure emanate from either the nuclear fission [18][19][20] or Gamow theory of α-decay [21][22][23][24][25]. The former relegates the idea of preformation; i.e., it is assumed that clusters are formed during the separation/deformation process of the parent nucleus while penetrating the confining interaction barrier. ...
... Here, our calculated P 0 values are in tune with the shell model, with notable minima around the magic numbers. This conforms with the recent findings of [24,25], in which it was demonstrated that P 0 can be influenced by the isospin asymmetry of the parents, the deformation of the daughter nuclei, and pairing and shell effects and that the minima of P 0 can be ascribed to the presence of proton, neutron shells and sub-shell closures. A careful evaluation of Figure 6, which portrays the relationship between the preformation probability P 0 and the penetrability P, where both parameters are shown as a function of the mass number, reveals that lower P 0 values correspond to a higher P and vice versa, such that their products P 0 P are near to the same order for all the decay chains under study. ...
A new α-emitting has been observed experimentally for neutron deficient 214U which opens the window to theoretically investigate the ground state properties of 214,216,218U isotopes and to examine α-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the α-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (Pα) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84≤Z≤90 and N<126, is normalised by an appropriately fitted neck-parameter ΔR. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10−5–10−8 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of α-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. α-particle clustering is largely influenced by the shell effect.
... This SLy4 parametrization effectively allows us to describe well the nuclear structure and nuclear matter properties [18,[34][35][36][37]. It is also widely used in the nuclear reactions [19,[38][39][40] and neutron stars [41,42] studies, and in the investigation of the α and cluster decays of heavy nuclei [13,20,43,44]. While the first term in Eq. (4) gives the direct part of the Coulomb energy, the second term accounts for its exchange parts in the Slater approximation [45]. ...
The isospin-asymmetry nuclear chains with N−Z from 2 to 60 are investigated to find the correlations of α-decay properties and isospin asymmetry. Both the proton- and neutron-skin thicknesses of α emitters belonging to different N−Z chains are tightly aligned along straight lines, the slope of which depends on the shell closure. For even-even α emitters, the neutron-skin thickness Δn multiplied by N−Z is a parabolic function of the isospin-asymmetry parameter I=(N−Z)/A. For the nuclei of incomplete neutron shells, the α-decay half-life Tα exponentially increases with Δn in the isospin chain. In the nuclei with valence neutrons and/or protons outside the magic core, Tα exponentially decreases with increasing Δn. The values of Tα and Qα are almost exponential functions of isospin asymmetry.
... Constructing a reasonable nuclear potential between an α-particle and a daughter nucleus is the most crucial issue in many α decay theoretical models, because the α decay half-life is mainly determined by the barrier penetrating probability [22]. There are many α decay models choosing different nuclear potentials between the αparticle and the daughter nucleus, such as the Coulomb and proximity potential model with proximity potential [23][24][25][26], the two-potential approach with a cosh parametrized form nuclear potential [27][28][29], the density-dependent cluster model with a double-folding integral of the renormalized M3Y nucleon-nucleon potential [30][31][32][33][34], the preformed cluster model with SLy4 Skyrme-like ef-fective interaction [9,35,36], and so on. ...
It is universally acknowledged that the Generalized Liquid Drop Model (GLDM) has two advantages over other α decay theoretical models: introduction of the quasimolecular shape mechanism and proximity energy. In the past few decades, the original proximity energy has been improved by numerous works. In the present work, the different improvements of proximity energy are examined when they are applied to the GLDM for enhancing the calculation accuracy and prediction ability of α decay half-lives for known and unsynthesized superheavy nuclei. The calculations of α half-lives have systematic improvements in reproducing experimental data after choosing a more suitable proximity energy for application to the GLDM. Encouraged by this, the α decay half-lives of even-even superheavy nuclei with Z=112-122 are predicted by the GLDM with a more suitable proximity energy. The predictions are consistent with calculations by the improved Royer formula and the universal decay law. In addition, the features of the predicted α decay half-lives imply that the next double magic nucleus after 208Pb is 298Fl.
... In addition to the leading effect of the corresponding Q α -values on the various α-decay modes of a given nucleus, it was reported that if the spin and/or parity assignments of the parent and daughter nuclei are different, then the probability of forming an α cluster on the surface of the parent is less than it would be if they have similar spin-parity [24]. Moreover, the angular momentum carried by the emitted α particle in the unfavored decays reduces its penetrability because it increases both the Coulomb barrier height and its width [24]. ...
... In addition to the leading effect of the corresponding Q α -values on the various α-decay modes of a given nucleus, it was reported that if the spin and/or parity assignments of the parent and daughter nuclei are different, then the probability of forming an α cluster on the surface of the parent is less than it would be if they have similar spin-parity [24]. Moreover, the angular momentum carried by the emitted α particle in the unfavored decays reduces its penetrability because it increases both the Coulomb barrier height and its width [24]. Conversely but less effectively, this angular momentum increases the knocking frequency of the α particle where it decreases the width of the internal pocket of the α + daughter potential and shifts its lowest point up. ...
... Conversely but less effectively, this angular momentum increases the knocking frequency of the α particle where it decreases the width of the internal pocket of the α + daughter potential and shifts its lowest point up. The nal effect manifests itself as a reduction in the decay width and a substantial increase in the partial half-lives against the unfavored decay modes relative to the favored ones [24]. The well-established hindrance of the unfavored decay modes between states of different spin and/or parity overcomes the enhancement from the expected increase of the Q α value of the odd-A nuclei relative to the even-even ones. ...
We investigate the change of the neutron-skin thickness from parent to daughter nuclei involved in the cluster decay process. The neutron-skin thickness is obtained using self-consistent Hartree–Fock–Bogolyubov calculations based on Skyrme-SLy4 effective nucleon–nucleon interaction. The experimental data of the cluster decay modes observed to date indicate that the shell effect then the released energy play the predominate role of determining the spontaneous cluster decay modes. The effect of the change in the neutron-skin thickness from parent to daughter nuclei comes next to them. The cluster decay preferably proceeds to yield the least possible increase in the neutron-skin thickness of the daughter nucleus ( δ n ). δ n decreases when the isospin-asymmetry of the emitted cluster increases. The relative stability of the radioactive nucleus and its corresponding partial half-life increase for the cluster decays leading to a significant increase in the neutron-skin thickness.
... The probability of cluster formation in the parent nucleus is described as the preformation factor, , including many nuclear structure information. It has became a prominent topic in nuclear physics [7][8][9][10]. ...
... Recent studies have been shown that the preformation factors are affected by many confirmed factors, such as the isospin asymmetry of the parent nucleus, deformation of the daughter, pairing effect, and shell effect [9,27]. It has been observed that the minima of the preformation factors are at the protons, neutron shells, and subshell closures [8,9,[28][29][30][31]. Moreover, many nuclear quantities [32][33][34][35][36], such as deformation and B (E2) values [32,33], rotational moments of inertia in low-spin states in the rare earth region [34], core cluster decomposition in the rare-earth region [35], and properties of excited states [36], display a systematic behavior with the product of valence protons (holes) and valence neutrons (holes) of the parent nucleus. ...
In the present work, a two-parameter empirical formula is proposed, based on the Geiger-Nuttall law, to study two-proton ( ) radioactivity. Using this formula, the calculated radioactivity half-lives are in good agreement with the experimental data as well as with calculated results obtained by Goncalves et al . [ Phys. Lett. B 774 , 14 (2017)] using the effective liquid drop model (ELDM), Sreeja et al . [ Eur. Phys. J. A 55 , 33 (2019)] using a four-parameter empirical formula, and Cui et al . [ Phys. Rev. C 101 : 014301 (2020)] using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible radioactivity candidates with radioactivity released energy , obtained from the latest evaluated atomic mass table AME2016. The predicted results are highly consistent with those obtained using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula.
... The probability of cluster formation in the parent nucleus is described as the preformation factor, , including many nuclear structure information. It has became a prominent topic in nuclear physics [7][8][9][10]. ...
... Recent studies have been shown that the preformation factors are affected by many confirmed factors, such as the isospin asymmetry of the parent nucleus, deformation of the daughter, pairing effect, and shell effect [9,27]. It has been observed that the minima of the preformation factors are at the protons, neutron shells, and subshell closures [8,9,[28][29][30][31]. Moreover, many nuclear quantities [32][33][34][35][36], such as deformation and B (E2) values [32,33], rotational moments of inertia in low-spin states in the rare earth region [34], core cluster decomposition in the rare-earth region [35], and properties of excited states [36], display a systematic behavior with the product of valence protons (holes) and valence neutrons (holes) of the parent nucleus. ...
In this study, we systematically investigate the decay preformation factors, , and the decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with being extracted from the ratio of the calculated decay half-life to the experimental one. The results show that there is a remarkable linear relationship between and the product of valance protons (holes) and valance neutrons (holes) . At the same time, we extract the decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun [J. Phys. G: Nucl. Part. Phys., 45 : 075106 (2018)], in which the decay was calculated by two different microscopic formulas. We find that the decay preformation factors are also related to . Combining with our previous studies [Sun , Phys. Rev. C, 94 : 024338 (2016); Deng , ibid. 96 : 024318 (2017); Deng , ibid. 97 : 044322 (2018)] and that of Seif [Phys. Rev. C, 84 : 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the decay preformation factor data calculated by the GLDM, we calculate the decay half-lives of these nuclei. The calculated results agree with the experimental data well.
... On the other hand, different analytic formulas have been proposed phenomenologically and applied systematically to analyze and predict the α decay preformation probabilities [31][32][33], taking into account the shell effect, pairing force, proton-neutron interaction, nuclear deformation, isospin asymmetry and so on. In addition, the N N p n scheme stresses the importance of the valence proton-neutron interaction on the evolution of collective behavior in nuclei. ...
We put forward a concise approach to calculate the α decay preformation probabilities by defining the microscopic valence nucleon and hole numbers based on the single particle energy spectra, which is obtained within the relativistic Hartree-Bogoliubov model. The residual interactions including neutron-neutron, proton-proton pairing and proton-neutron correlations could trigger the collective motions among the valence nucleons and holes, along with the independent particle motions under the mean field assumption. Therefore the more the number of valence nucleons and holes, the stronger the collective motions such as α particle clustering. We assume that the valence orbits locate around the Fermi surface obeying a Fermi-Dirac distribution, i.e. nucleons (holes) occupying the orbits with much lower (higher) energies away from the Fermi surface can not be considered as the valence nucleons (holes). The α decay preformation probabilities Pα are calculated within the Np Nn scheme in terms of the valence proton-neutron interaction. As an example, in the case of even-even polonium, radon, radium and thorium isotopes the extracted α decay preformation probabilities , which are obtained within the generalized liquid drop model, can be well reproduced by employing two different formulas to take into account the shell effect at N = 126 shell closure.
... The differences in these properties from parent to daughter nuclei in addition to the released energy define the decay mode. For α decay, the preformation probability of α cluster, its assaulting frequency, and penetration probability are also important to define the half-life time T α [24][25][26][27]. ...
... In the framework of the preformed cluster model, the αdecay half-life can be obtained in terms of the preformation probability (S α ), the assault frequency (ν), and the penetration probability (P) of the emitted α particle as [24,25] T α =h ln 2 S α νP . ...
... The details of the method of calculation are given in Refs. [23,24]. ...
The change of proton and neutron skin thicknesses is investigated in nuclei after α decay. The skin thicknesses are self-consistently calculated. The observed α decays lead to relatively large decrease of the proton skin in the daughter nuclei. A large increase of the neutron skin in the daughter nucleus reflects the hindered α decay. This hindrance is related to the decrease of both the Qα value and the preformation probability in the parent nucleus. For each isotopic chain, the observed half-lives consistently correlate with the change of the proton (neutron) skin thickness, from parent to daughter nuclei.
... Nevertheless, we rarely know formation and movement of the α particle inside the parent nuclei, as a result of the complicated structure of quantum many-body systems. Therefore, there are a few works [15][16][17][18] studying α preformation probabilities from the viewpoint of microscopic theory. Phenomenologically, α preformation probabilities are obtained by the ratios of theoretical calculations, without considering the preformation factors, to experimental half-lives [19][20][21][22]. ...
... Phenomenologically, α preformation probabilities are obtained by the ratios of theoretical calculations, without considering the preformation factors, to experimental half-lives [19][20][21][22]. Recent research has shown that the pairing effect, the shell effect, and different spin-parity states of daughter and parent nucleus are the major factors determining α preformation probabilities [17]. Seif et al. have proposed that the α preformation probability, considering isospin, shell effect, and valence proton-neutron interaction, is proportional to N p N n for even-even nuclei around proton Z = 82, neutron N = 82 and 126 shell closures [7], where N p and N n denote valence protons (holes) and valence neutrons (holes) of the parent nucleus, respectively. ...
In the present work, the unfavored α-decay half-lives and α preformation probabilities of closed-shell nuclei related to ground and isomeric states around Z=82, N=82 and 126 shell closures are investigated by adopting the two-potential approach from the perspective of valence nucleon (hole) and isospin asymmetry of the parent nucleus. The results indicate that α preformation probability has linear dependence on NpNn or NpNnI, the same as the case of favored α decay in our previous work [X.-D. Sun et al., Phys. Rev. C 94, 024338 (2016)]. Np, Nn, and I represent the number of valence protons (holes), the number of valence neutrons (holes), and the isospin of the parent nucleus, respectively. Fitting the α preformation probability data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two linear formulas of the α preformation probabilities and the values of corresponding parameters. Based on the formulas and corresponding parameters, we calculate the α-decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.
